THURSDAY, SEPTEMBER 6, 1906.

NILE STUDIES.

The Physiography of the River Nile and its Basin. By Captain H. G. Lyons, Director-General, Survey Department. Pp. viii+411; with 48 plates. (Cairo: National Printing Department, 1906.)

WHEN

WHEN a British army was first sent to occupy Egypt, the late Prof. Huxley called upon the Royal Society to appoint a committee to arrange for a systematic study of that most interesting country. He justly pointed out how much the French Government had accomplished in the promotion of scientific research and in the publication of its results during their short period of occupation at the beginning of last century, and he declared that it would be a national disgrace if we failed to accomplish something of the same kind with our much greater opportunities.

The publication of the work before us, and of others of a similar character, serves to show that England has not been unmindful of her responsibilities or neglectful of the opportunities which have resulted from our close association with the Egyptian Government for more than two decades. Captain Lyons, who organised the Geological Survey of Egypt-some of the admirable publications of which have been reviewed in the pages of NATURE-has now become head of the whole Survey Department of Egypt, and is administering its affairs with characteristic energy and ability.

The discovery of the Lake district of Equatorial Africa by Speke and Grant, with the surveys and observations of Gordon, Emin, Schweinfurth, Junker, and others, has afforded a safe basis for the treatises on Nile hydrography by Klöden, Lombardini, Chavanne, and de Martonne; but since the fall of Omdurman in 1898, and the consequent opening up of the Sudan, much new material has been made available. Systematic meteorological records have been collected at various stations in Uganda, Abyssinia, and the Sudan, and careful measurements have been made of the levels, at different seasons of the year, of the several lakes and of the amount of water discharged by each of the Nile tributaries. All these sources of information have been admirably utilised by Captain Lyons in his survey of the present state of our knowledge of Nile hydrography.

After a very interesting discussion of the climate and rainfall of the districts from which the waters of the Nile are supplied, Captain Lyons proceeds to describe in detail the eight regions into which the Nile basin may be conveniently divided. Recent surveys in most of these districts have given much greater precision to our knowledge of their physiography, geology, meteorology, and other natural features.

The Lake Plateau, which has an average elevation of about 5000 feet, is composed of various metamorphic rocks. The central part of the area is occupied by the great Lake Victoria, while in its western part is the deep rift valley with Lakes Albert

Edward and Albert. The district is characterised by rapids and marshes, no regular flow of the streams having been established by erosion, but the effective supply to the Nile from the Victoria Lake varies from 500 cubic metres to 1000 cubic metres per second.

The basin of the Bahr el Jebel, Bahr el Zaraf, and Bahr el Ghazal, although having a very heavy rainfall, really absorbs, not only this, but a considerable part of the water supplied to it from the Lake Plateau. The rivers wind through level alluvial plains, and support a great marsh vegetation (the "sadd "), consisting of papyrus and various reeds with some floating plants, and evaporation and absorption by vegetation take up, not only the whole of the considerable rainfall, but diminish the amount coming from Lake Victoria by from 4 per cent. to 52 per cent.

The Sobat Basin is occupied by a comparatively short river with a rapid fall, and adds an appreciable but varying amount to the waters coming down the White Nile.

In the White Nile Basin we find that we have the most constant element in the supply of the Nile waters. The 1500 million cubic metres of water from the Sobat flood are supplied to the Nile during October, November, and December, thus modifying the fall in the water-level of the river during those months.

The Blue Nile, the Atbara, and the Khor el Gash.— These rivers drain a plateau with an elevation of from 6000 feet to 10,000 feet. Although exact information concerning the distribution of rainfall in various parts of the Abyssinian highlands is still wanting, there can be no doubt that the rainfall is very great. The regular northward movement of the rain-belt during the monsoon season leads to the flooding of the Blue Nile and Atbara, and the annual Nile flood in July, August, September, and October. The volume and continuance of this flood are clearly dependent, firstly, on the amount of rainfall in the Abyssinian highlands, and secondly, on the great length of the river courses, with their deeply-cut channels, ensuring a regulation of the water supply during torrential rains. Captain Lyons directs attention to the possible interference with this latter element in the production of the periodic Nile floods, which may result from the extensive afforestation which is said to be going on in Abyssinia.

From Khartoum and Berber to Aswan the united waters of the White Nile, Blue Nile, and Atbara flow in a single stream, which is eroding its bed with considerable rapidity, there being some cataracts but no flood plains. The waters of the Nile have in this part attained their maximum, and in its course northward the river is constantly losing by evaporation and the withdrawal of its waters for irrigation.

From Aswan to Cairo the Nile flows in a depression in which it has deposited a considerable thickness of alluvium, and the river winds through the flood plains thus formed. During the fifty centuries of which we have a record, the Nile appears to have deposited a thickness of 16 feet or 17 feet of alluvium in this part of its course, and the silting up of various water

channels and the reclamation of land in consequence have resulted. It is in this way that the lake occupying the depression of the Fayum has been diminished in area.

The floods in the Nile Delta of which records have been kept, that are trustworthy for the past 175 years at least, have been critically studied by Captain Lyons with the view of discovering the determining causes of their variations. While no regular periodic alternations of high and low floods can be detected by the study of these records, their dependence on the rainfall and the distribution of atmospheric pressure in the highlands of Equatorial Africa is very apparent. There is reason to believe that more numerous, systematic, and complete meteorological observations in the districts outside Egypt may enable us, in the end, to predict from month to month the probable fluctuations of the annual Nile flood.

The space at our command has only permitted the notice of a few of the more salient features of this very interesting volume. In conclusion, we must congratulate Captain Lyons and the Egyptian Government upon the great amount of valuable work which | has been accomplished and is still in progress. A word of praise must also be added on the excellent typography of the volume, and the admirable plates with which it is illustrated. J. W. J.

THE HISTORY OF DETERMINANTS. The Theory of Determinants in the Historical Order of Development. Part i. Second edition. General Determinants up to 1841. Part ii. Special Determinants up to 1841. By Dr. T. Muir, C.M.G., F.R.S. Pp. xii+492. (London: Macmillan and Co., Ltd., 1906.) Price 178. net.

A

MATHEMATICAL history of the right sort is much more than a mere bibliography, and in some respects is more valuable than a treatise on the

subject with which it deals. It helps us to see how mathematical ideas originate, and how, as they become familiar, the symbolism by which they are expressed becomes compact and appropriate. This is especially the case with determinants, because a determinant is essentially a comprehensive symbol, and it would perhaps be more proper to speak of the calculus than of the theory of determinants. It may seem strange, at first sight, to find a history so large as this dealing with a subject so limited; but no one can complain that the author is either diffuse or irrelevant, and his work may be praised without restriction as a model of its kind.

It is unnecessary to say much of the first part, which is mainly a reprint of the volume which appeared in 1900. Dr. Muir has written a new introduction, and added a few additional notices. Two things cannot fail to strike the reader of this part. The first is the great supremacy of Cauchy and Jacobi in everything relating to choice of notation and clearness of statement; the other is the great and long unrecognised ability of Schweins. Schweins, in a way, brought this fate upon himself; his style is

heavy, and his notation cumbrous in the extreme, but his contributions to the subject are of great value and generality, although they attracted no notice for many years, and were re-discovered by others. Unfortu nately, they are expressed in such a repulsive notation that no one but an enthusiast would read his works. and the student will feel very grateful to Dr. Muir for his analysis of them. Part of this analysis, in some ways the most interesting, is given on pp. 311322; this, and the subsequent section on a paper of Sylvester's, deserve careful reading, because, as Dr Muir points out, Schweins gives some results on alternants which even now are not familiar, and Sylvester makes some hasty statements which, as they stand, appear to be incorrect, but which, if corrected, or rightly interpreted, might lead to importanı formulæ.

It should be noted that on p. 323 the determinant is misprinted, a, a2, &c., being put for a,, a,, &ề Moreover, it is not explained so clearly as it should be that aa,; while the law a,. a, a,,, is not used The right statement is (a* . a®) = {(a* + *) = a,.,; whit 【(a^)5(aa) = a‚a‚§. Readers of Sylvester's papers must be careful to distinguish this from the square of the operator It may be noticed, in passing, that these generalised alternants present themselves in the theory of numbers, both when the elements arr roots of unity and also when they are not, so tha further knowledge of their properties is desirable, and the suggestion made (p. 325) that Sylvester's results are true when the elements are periodic deserves further examination.

Considerable space is given to functional and orthogonal determinants, and here, of course, Jacobi receives most attention. The results are now familiar that it requires some effort of imagination to realise the gain in working power which has resulted from Jacobi's investigations. In this connection attention may be directed to an odd remark on p. 247 Speaking of one of Jacobi's papers, Dr. Muir says."The only thing worth noticing is the curious cubi equation . . ."; this "curious" equation is nothing more nor less than the reducing cubic for two ternars quadratic forms, in the exact notation of Salmon's "Conics"! And Dr. Muir even takes the trouble to express the invariants e, e' in the forms

as if this were a quite novel idea.

Returning for a moment to alternants and their applications, attention may be directed to the work of Jacobi and Cauchy on the expansions of rational functions of several variables (pp. 331-345). This is important in the theory of functions, in that of algebraic forms, and in that of partitions. In some ways it deserves further investigation; in various applications the expansions have to be infinite series and the question of convergency has to be faced, eve when the series are used for establishing formal equvalences; this is a curious case of formal and arithmetical algebra each marching, so to speak, on the other's domain.

There is one more observation made by Dr. Muir (p. 290) which is rather puzzling. After giving some identities of Lagrange's, which are, in fact, relations between determinants, Dr. Muir says, "a reference to the original papers, already described, will make it almost perfectly certain that Lagrange did not view them in this light. The like is true of Gauss. . . .' Now Gauss, at any rate, used the term "determinant"; if this word is used in the modern sense of the symbol, of course Dr. Muir's remark is correct, but is then quite trivial; on the other hand, if it means the function, it is hard to see how Gauss, not to say Lagrange, could fail to see that their expressions involved determinants, especially as each was quite familiar with them in connection with the theory of numbers. This is particularly true of Gauss, who gives the name "determinant" to (aby) as well as to (aB).

It is a matter of regret that, although a bibliography of orthogonants (to 1840) has been given, Dr. Muir has not been able to include in this volume his valuable lists of writings relating to determinants. To have added them would not have increased the size of the book very much, and it would have been very convenient to have them here. But perhaps the author intends to give us the history of his favourite subject subsequent to 1841, the date at which he has now closed. G. B. M.

EUROPEAN VERTEBRATES.

Die wirbelthiere Europa's mit Berücksichtigung der Faunen von Vorderasien und Nordafrika. By Dr. O. Schmiedeknecht. Pp. vi+ 470. (Jena: Gustav Fischer, 1906.) Price 10 marks.

IT

T is always convenient to have within covers separated by a moderate distance only an account of the fauna of a definite district, especially when, as in the present instance, the fauna is one that is fairly exhaustively known. It is not likely that a manual of the scope of that which we review here will ever need substantial alteration, or even slight changes, for many years to come. The volume, in fact, is not only of permanent value, but contains the marrow of a whole library of faunistic works, and includes all that the student needs, whether the aim of his studies be purely geographical or whether he desires a handy series of definitions of families, genera, and species. Inasmuch as the volume is something less than five hundred pages in length, and seeing that the definitions of family and other characters are often from twelve to twenty lines in length, the author is compelled to deny himself any discussion of points round which opinions fluctuate, and is driven to be entirely dogmatic.

It is therefore not everyone who will follow Dr. Schmiedeknecht with complete agreement from beginning to end. He will not, for example, please all of us by placing the "reed pheasant," Panurus biarmicus, among the tits, though it is frequently called the bearded tit; nor can we agree to the use

of four separate generic names for the four species of rorquals, which appears to us as a recrudescence of one of the very worst achievements of the systematists of the past. In adopting an old scheme of arrangement for birds, the author is compelled thereby to separate widely the gulls and Limicoline birds, which many anatomists have concurred in placing in very close relationship. There are plenty of similar examples to be gathered from Dr. Schmiedeknecht's pages. If the author errs at all in the number of species which he admits into his manual, it is rather on the side of economy than profusion. Of the very long series of "species" of mice admitted, or rather insisted upon, by some British naturalists, Dr. Schmiedeknecht will only consider four as established. Perhaps he carries this plan a little too far in declining to admit the "Irish weasel," Mustela hibernica, which is not in any way referred to. Apropos of weasels, it will certainly surprise some persons to learn that the proper name of the common weasel is not Mustela vulgaris, but M. nivalis, inasmuch as (according to Dr. Schmiedeknecht) Linnæus gave the name to an individual in winter dress.

That the weasel, like its very close ally the stoat, changes to white in winter can hardly be a fact of general knowledge, since it is not mentioned in at any rate one well-known work upon British mammals.

In classifying the snakes, Dr. Schmiedeknecht follows a somewhat curious plan. He divides the European species into five families of equal rank, which are (in the order treated by him) Crotalidæ, Viperidæ, Colubridæ, Peropodidæ, and Typhlopidæ. To give the "pit vipers " a place in the system which divides them as far from the more typical Viperidæ as from the Peropodidæ, or Boidæ as most would prefer to call them, is quite opposed to the minute details of anatomical agreement between all vipers.

To such criticisms, however, the author might well reply that his arrangement is rather a sorting than a classification, and that, as a matter of fact, judged by external characters only (and it is these alone that are made use of), the two divisions of the vipers are very distinct, and the gulls are remote from the sandpipers, plovers, &c.

In his preface, Dr. Schmiedeknecht puts himself forward as a champion of the systematic aspect of zoology as a desirable commencement for the student of that science There is no doubt that most of us, in this country at least, were led to pursue zoological studies by reason of the fervour and enthusiasm engendered by the joys of collecting objects of natural history. The quality of knowledge possessed by the pure systematist of mature years is often but little in advance of this stage, and in remarking that "he must be as a rule a remarkable systematist who is not at the same time a biologist," the author is expressing an opinion which the annals of museums do not confirm. In fact, Dr. Schmiedeknecht's introductory remarks read a little like an apology, which is not at all needed in introducing so useful and accurate a work as that which we notice here. F. E. B.

Refraktionstafeln. By Dr. L. de Ball, Direktor der v. Kuffnerschen Sternwarte. Pp. xiv+18. (Leipzig: W. Engelmann, 1906.) Price 2.40 marks. THE methods of computing corrections for atmospheric refraction have always been more or less unsatisfactory. The conditions of the problem do not lend themselves to extreme accuracy on account of the uncertainty of the meteorological elements introduced. The determination of the density of the atmosphere at any precise moment, dependent as it is on the temperature, the amount of aqueous vapour present, and other conditions, is not simple, and custom and authority alike have sanctioned the employment of rough and approximate data. Bessel's tables, so long in use, were admittedly founded upon inadequate material, and probably would have long since been superseded but for the inconvenience that arises when any breach of continuity occurs in a long series of observations; but in observatories where measures of zenith distance have been made at small altitudes this inconvenience has had to be faced. At Greenwich, for example, corrections to Bessel's tables, or Airy's modifications of them, have been alternately introduced and rejected in the treatment of observations at large zenith distances.

In the tables which Dr. L. de Ball has issued the difficulty of continuing an unbroken series of corrections, available from the zenith to the horizon, has not been attempted. The tables as arranged are available up to 75° zenith distance, and within this limit represent a consistent theory, that of M. Radau. The form in which the tables are constructed gives the log. of the refraction presumably correct to four places of decimals. In the example worked out it has been necessary to take out five significant integers, and, if the second decimal place is to be correct, this may be rather a severe strain on four-figure logs.; but Dr. L. de Ball gives very good and sufficient reasons for not extending the tables beyond these limits. He reminds us that the determination of the temperature of the air is not so easy as the reading of a thermometer seems to suggest. The thermometer bulb is affected by the heat rays emitted by the objects which surround it, whilst the air absorbs only a part of those rays. On these grounds the temperature indicated by the thermometer may easily differ o°.2 C. from that of the atmosphere, and such a difference would occasion an error of three units in the fourth decimal of the log. of the density, and a similar amount in the log. of the refraction. The tables aim at giving an accuracy which is sufficient and practical rather than making a claim to extreme and misleading rigour. A further proof that the author has considered the practical side is shown by the fact that he has included tables designed to assist the computation of differences of refraction, applicable to the reduction of heliometer and photographic observations. The Butterflies of the British Isles. By Richard South, F.E.S. Pp. x+204. (London: Frederick Warne and Co., 1906.) Price 6s. net. NOTWITHSTANDING the large number of books relating to British butterflies, there was still room for pocket handbook which should do for the present generation what Coleman's "British Butterflies did for the last, and this want Mr. South has set himself to provide. He has succeeded in giving us a portable little book, well up to date, containing full

a

&c., besides a good account of the individual species.. The plates contain coloured figures of the butterflies. on one side of the page, and plain figures of caterpillars, &c., on the back, thus doubling the number of page illustrations without adding to the thickness of the book. The illustrations in the text are nearly

all in the introduction. They are uncoloured, and some of them are taken from Sharp, Aurivillius, and other trustworthy authorities.

Mr. South admits sixty-eight species as British, but regards only fifty-seven of these as actual natives; but surely, though some of the remainder are extinct, and others only casual visitors, the black-veined white (once abundant, but now almost extinct in England), and the red admiral, still one of the commonest of the Vanessidæ, ought to have been included among the genuine natives. The evidence against the red admiral being a genuine British species seems the assumption of its being a migrant, abundantly in the case of its nearest ally, the painted though this is admittedly not proved, as it is

rest on

lady.

to

The rapid disappearance of butterflies in England is doubtless largely due to the wholesale clearing away of the weeds and plants on which the caterpillars feed, by the utilisation of every scrap of waste ground. Yet this cannot be the only reason, or the black-veined white, which feeds on hawthorn as well as on fruit trees, would not be disappearing. In this case the disappearance of the butterfly seems to be due to the increase of insect-eating birds. Every fresh book on butterflies records the increasing scarcity of many species once common, and there are only a few, such as the clover-feeding clouded yellows, which are more plentiful now than in former days.

In the case of the smaller and more variable butter

flies, a considerable number of varieties are figured (sometimes as many as seventeen on one plate), and we think that most entomologists who are interested in British butterflies will find Mr. South's little book a very useful supplement to any they may already happen to possess on the same subject.

W. F. K.

LETTER TO THE EDITOR. [The Editor does not hold himself responsible for opinions expressed by his correspondents. Neither can he undertake to return, or to correspond with the writers of, rejected" manuscripts intended for this or any other part of NATURE. No notice is taken of anonymous communications.]

The Latest Critic of Biometry.

MR. J. J. LISTER in his presidential address to Section D at the British Association felt it his duty to go somewhat out of his way in order to urge on biometricians "that the old adage should be borne in mind recommending that before beginning culinary operations it is advisable first to catch your hare, in other words, to make sure that the problem you seek to elucidate is sound from the standpoint of biology before bringing a formidable mathematical apparatus into action for its investigation" (NATURE, August 16, p. 400). The importance of the occasion no doubt prevented Mr. Lister from illustrating his criticism; he had much else to deal with, and he probably hoped that his words without detailed proof would have all the weight which attaches to presidential utterances. These are not made without careful thought and proper study. But in order that a criticism of this kind should be effective,

biometricians need more information, and they recognised that Mr. Lister could hardly refuse to cite instances of the

type of work which led to his advice.

Hoping that we might profit by Mr. Lister's caution, I wrote to him as soon as I read his paper in your columns asking for definite instances upon which we might considerhow to amend our courses. He has kindly consented to